If the hypotenuse of a triangle is 12 cm and

Brooklyn1wp 2022-02-28 Answered
If the hypotenuse of a triangle is 12 cm and the measure of its legs are in the ratio 1:2, then what are the measures of it’s legs?
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Expert Answer

bedevijuo3e
Answered 2022-03-01 Author has 6 answers

Step 1
Here is a way to solve without directly using Pythagoras theorem.
Let a, b and c be the side lengths of the given right triangle such that c is is the length of hypotenuse.
Measure of legs are in the ratio 1:2
Let a=x, b=2x
Let R and r be the circumradius and inradius of right triangle respectively.
R=c2=122=6
r=aba+b+c=x×2xx+2x+12=2x23x+12
We have,
R+r=a+b2
6+2x23x+12=x+2x2
(3x+12)(3x12)=4x2
5x2144=0x=125
a=125
b=2×125=245

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junoon363km
Answered 2022-03-02 Author has 8 answers
Step 1
If the triangle has a hypotenuse, I’ll assume that the triangle is right angled.
Mr. Pythagoras says that the hypotenuse squared = leg 1 squared plus leg 2 squared.
leg 1=1x
leg 2=2x
leg 12+leg 22=hypotenuse2
(1x)2+(2x)2=122
(1x2})+(4x2)=144
5x2=122
x2=1445
x2=28.8
x=5.367 cm
2x=2×5.367=10.733 cm
Step 2
Proof:
If both sides of this equation are equal, then the answer is right.
122=≠5.3672+10.7332
144=≠28.8+115.2
144=144
One leg of the triangle is 5.367 cm and the second leg is 10.733 cm.
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